Chapter 6
Section 6.1
2 thirds
2 out of 3
2 over 3
2 divided by 3
2
3
1
4
2
4
3
4
4
4
Accurately shade the following:
1
2
2
4
3
6
4
8
1
Discrete quantities- countable objects
Continuous quantities- measured objects
Which makes more sense: 1/5 of a class of 24 or 1/5 of a foot or 1/5 of an apple?
why?
What does each saying mean?
Does 1/6 of a class of 24 make sense? why?
Give an example of when 1/5 of a person makes sense?
Discuss the following:
2
𝒂
𝒃
The part-whole (portion of a whole/s) meaning for the fractions:
EX/ Three fifths of an apple. 4 of the 7 players.
1) The whole unit is being pictured: The apple, the inch, the meter, or sandwich/s will be cut the into
equal pieces. The entire team or the entire class or a box of bats.
2) The numerator gives you the number of equally cut pieces or a number of objects.
3) The denominator gives you the equal cut size or the total number of possible objects.
2
Show me 5 of the continuous quantity using equal parts.
2
Show me 5 of three different discrete quantity. ex/ 2/5 of a 5 person team.
The "Sharing Equally" view: Represents
𝑎
𝑏
as 𝑎 ÷ 𝑏.
𝑎
𝑏
is read "a" objects shared equally with "b"
people.
(𝒕𝒐𝒕𝒂𝒍 𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒊𝒕𝒆𝒎𝒔) ÷ (𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒈𝒓𝒐𝒖𝒑𝒔) =
(𝑵𝒖𝒎𝒃𝒆𝒓 𝒊𝒕𝒆𝒎𝒔 𝒊𝒏 𝒆𝒂𝒄𝒉 𝒈𝒓𝒐𝒖𝒑)
6
=
6
÷
2
=
2
3
=
4
3
÷
4
=
3
3
4
3
Use the fraction rectangles to show the following on the back side of this paper:
1) The part-whole (portion of a whole/s) meaning for the fractions:
3
2
2
2
5
a)
b)
c)
d)
e)
4
3
5
4
8
2) The "Sharing Equally" meaning for the fractions (you will need to combine your forces):
3
2
2
2
5
a) 4 b) 3
c) 5
d) 4
e) 8
3) The part-whole (portion of a whole/s) meaning for the fractions:
5
1
a) 4 b) 1 4
4) The "Sharing Equally" meaning for the fractions (you will need to combine your forces):
5
4
5) Decide which is larger.
a)
d)
3
4
3
4
or
or
7
b)
8
2
e)
4
6) How much bigger is
2
3
from
1
2
7
8
or
or
5
c)
8
2
3
or
7
12
7
12
1
2
7) The following candy bar is 2/3 of a regular bar. Draw the original bar.
2
8) The following carpet is 3 5 feet long. Drawing as carefully as you can the following using the carpets
measurements.
a) 4 feet
1
b) 1 2 feet
9) Draw the following in mixed form and then in improper fraction form. Use the standard method for
converting mixed numbers to verify your answer.
3
a) 2 5
2
b) 1 3
4
6.2 Equivalent fractions
Section 3.2: Equivalent fractions
Use the fraction rectangles to find two or more equivalent fractions for each:
2

3
1

2
4

12
1
3 person group work.
1) Find the matching equivalent fractions.
𝑎)
2
=
5 10
2) Find three equivalent fractions for
3) Find three equivalent fractions for
𝑏)
6 36
=
7
𝑐)
10
=
35 7
3
.
8
24
.
36
5
2
4) Circle the fractions that are equivalent to
5
6
12
.
18
40
14
35
5) Costco slices it's pizza in to 6 slices. Each slice is to large for a normal person to consume.
a) What fractional size is each slice?
b) If you purchased a 6 slice pizza, then each slice is _______. If you ask for a knife and start slicing the pizza
again into equal size slices, then name two more fractional size slices you could create with your plastic knife.
6) Waste paper basket game. Step 1: make notebook paper basketballs. Step 2: Player one gets two shots.
Player two gets three shots. Player three gets six shots. Step 3: Shoot baskets and record how many each
player makes. Who performed the best?
7) find
15
8
inches,
4
1
inches,
inches,
4
16
20
16
inches,
7
2
inches
8) Decide which is larger.
a)
d)
3
4
3
4
or
or
7
8
2
4
b)
e)
1
2
7
8
or
or
5
8
c)
2
3
or
7
12
7
12
6
Reducing fractions
Simplify
24
60
How to find the GCF
1. 18, 24 Using factors
2. 18, 25 using factor trees
3. Ladder method.
18
9
3
100
24
12
4
2
3
GCF= The product of the common factors=
23  6
40
GCF= The product of the common factors=______=
This method works all the time with two numbers. It will not work all the time with more than two
numbers you will have to think. Find the GCF and LCM for the following:
1) 18
8
2) 36 64
3) 18 45
4)
9 7
7
Simplify the following:
1)
25
75
2)
151
6
3)
36
16
4) A group is made up of 4 boys and 6 girls. What simplified fraction of the group are boys? Show that
simplifying process using pictures or letters. Hint: BBBBGGGGGG BB BB GG GG GG
5) A group is made up of 3 boys and 9 girls. What simplified fraction of the group are boys? Show that
simplifying process using pictures or letters.
6) What is connections can you make between the math behind the problem and the pictures.
7) Show the following using pictures for the context given.
a)
3
4
9
= 12
Sticks
b)
10
20
2
=4
marbles
c)
12
18
2
=3
your choice
8
Section 6.3
Review of your past knowledge:
Now get into groups and try the following using your calculator:
9
Fractions into Decimals:
A fraction in simplest form can be represented by terminating decimals, no vinculum, when the
denominator has only 2's and 5's as factors. Why?
Hint: Write 0.33 as a fraction. Write 0.00231 as a fraction.
A fraction in simplest form can be represented by repeating decimals, vinculum, when the
denominator has a number other than 2's and 5's as a factor.
Find the decimal form of the following:
𝟏
𝟗
𝟐 𝟑 𝟒 𝟓 𝟔 𝟕 𝟖 𝟗
,𝟗,𝟗,𝟗,𝟗,𝟗,𝟗,𝟗,𝟗
Find the decimal form and remainder form of the following:
Find the decimal form and remainder form of the following:
𝟏
𝟑
𝟏
𝟓
𝟐 𝟑
,𝟑,𝟑
𝟐 𝟑 𝟒 𝟓
,𝟓,𝟓,𝟓,𝟓
Can you see a pattern?
How many possible remainders can you get with each?
How many possible remainders can you get when you have 7ths? How many types of repetition
with 7ths?
10
Decimals into Fractions:
Terminating Decimals:
Decimal to Fraction:
0.6 =
0.65 =
0.654 =
1.6 =
12.65 =
123.654 =
0.0006 =
1.0065 =
1000.004 =
Write the following fractions as decimals:
5
=
10
2
=
10
3
=
100
923
=
1000
Repeating decimals:
21
=
100
𝟐
𝟗
=
𝟑𝟓
𝟗𝟗
=
𝟏𝟕𝟒
𝟗𝟗𝟗
𝟐. ̅̅̅̅
𝟑𝟓
𝟐. ̅̅̅̅
𝟑𝟓
̅̅̅̅̅̅
𝟎. 𝟓𝟔𝟕
̅̅̅̅̅̅
𝟎. 𝟓𝟔𝟕
̅
𝟏. 𝟕𝟒
̅
𝟏. 𝟕𝟒
=
𝟓𝟏
𝟗𝟗𝟗
=
𝟑𝟓
𝟗𝟗𝟎𝟎
=
11
NATURAL NUMBERS (counting numbers)
1, 2, 3, 4, 5,…
1 2 3 4 5 6 7 8 9 1
WHOLE NUMBERS 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, …
0 1 2 3 4 5 6 7 8 9 10
INTEGERS…-3, -2, -1, 0, 1, 2, 3, …
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
RATIONAL NUMBERS Integers, Repeating and ending Decimals, and Fractions -3, -2
7
, 0, 3, 5.7,
8
4.33333…
-5.5
0
1
1
2
IRRATIONAL NUMBERS
Decimals that don’t repeat or end. We don’t know exactly where they are on the number line. Like
radicals,  ,
1.235698425624… there is no pattern.
REAL NUMBERS
All of the previous numbers
RATIONAL
INTEGERS
WHOLE NUMBERS
NATURAL
REAL
IRRATIONAL
2,
3,  1, 0.5, 234.12, 0, 3 , 
List all of the numbers that are:
1) whole numbers
2) Irrational
3) Rational
4) Real
12

Decimal
Percent
Mixed number/fraction
.23
2
5
3
4
33%
22.5%
.515
350%
0.005%
̅̅̅̅
2. 35
21
100
35.1
1
33 %
3
1
5 %
4
2
3
Exact fractional percent
5
2
25
1. 8̅
13
Section 6.4
Some rental companies will only rent, if the renter's monthly rent is 1/2 the renter's monthly income.
If the renter's income is $2325, about how much monthly rent would he be allowed?
If a statistician took over a rental company, the new fraction might be 467/1253. About how much
monthly rent would he be allowed?
What fraction is the 21/29 close to?
0
1
2
1
3. Find a number that is between each fraction above.
14